Calculation: FEM structural analysis/ optimization

The FEM strength analysis (finite element method) is a numerical method for the computational investigation of mechanical stresses and deformations in components under various loads. It is used to simulate the structural behavior of complex geometries under realistic boundary conditions in order to identify weak points and critical areas at an early stage. The strength verification is the mathematical or experimental proof that a component can withstand the expected stresses over its service life without failure. In the combination of both methods, occurring stresses are compared with the permissible load-bearing capacity, whereby safety factors are taken into account. This is essential for ensuring safety and reliability and for implementing an economical lightweight design.

FEM-based topology optimization is a computer-aided method for structural component optimization in which the optimum material distribution across main load paths in the specified installation space is determined on the basis of load cases, boundary conditions and design objectives. The aim is to use material specifically where it is needed for force transmission and at the same time to save mass in less stressed areas. This supports holistic lightweight construction in particular, as aspects of structural lightweight construction are taken into account, whereby the focus is often on optimizing the stiffness distribution and the integration of surface support structures must be carried out separately. Stress, stiffness or frequency analyses are often integrated at the same time. This makes it possible to generate innovative topological structural lightweight construction concepts at an early stage in the development process, which specifically improve weight, costs and sustainability. The optimization process is used, for example, in the field of additive manufacturing, structural optimization of cast components, frame structures, articulated trusses and space frames as well as injection moulded components.

The aim of topography optimization is to create thin-walled structures, whereby stiffness and stress distributions or other mechanical boundary conditions remain the same or are improved. Thin-walled structures are often designed with surface structures. Here, multi-dimensional elevations, bead arrangements or dies are often used as reinforcing elements. For a given set of surface structures, topography optimization technology generates innovative design proposals with an optimal structure pattern and optimal locations for reinforcements. Typical applications include the reinforcement of cladding, shear panels, buckling stiffeners as well as the optimization of vibration behavior and NVH.

FEM stiffness optimization is a computational method for the targeted increase or adjustment of component stiffness (EI) using finite element analysis (FEM) without using unnecessary mass or material. The aim is to achieve an optimum ratio between installation space, weight and function within the specified stiffness corridor through intelligent geometry or material adjustments. In terms of holistic lightweight construction, not only is the local deformation minimized, but the stiffness-driven system effect, interface loads and influences on adjacent components are also taken into account. Stiffness optimization is often carried out via topology or shape optimization and is closely linked to mass distribution, installation space restrictions and production technologies. Typically, stiffness optimization is carried out, for example, in bending and torsionally stiff support structures.

FEM-based stress optimization is a structural optimization method that uses the finite element method (FEM) to analyse and specifically improve stress distributions in components. Bionic-based optimization methods such as SKO and special shape optimization methods are used here. - The aim is to reduce stress peaks and to design the material distribution in such a way that the existing load (strain energy distribution) is carried as evenly as possible. The geometry, wall thicknesses or reinforcements are adapted in such a way that critical stresses remain below permissible limit values. The process enables more precise utilization of material properties and contributes significantly to weight reduction in stress-driven structural systems. Stress optimization is particularly relevant in lightweight construction, as it can simultaneously improve safety, service life and resource efficiency. Stress optimization is typically performed on structures and components with local load application, bearing points, bolt-on points and systems that are subject to fatigue and vibration stresses.

FEM-based generic investigations are simulation-based structural optimization methods in which the finite element method (FEM) is used to systematically analyse the mechanical behaviour of a component under varying boundary conditions, load cases and design parameters. The aim is not only to evaluate an existing design, but also to derive fundamental interactions for optimizing the structure in terms of weight, stiffness, strength or natural frequency. Unlike classic FEM analyses, which check a defined geometry model, generic analyses use parametric geometries or topology approaches to explore variant spaces. This allows robust, load-path-compatible designs to be identified - regardless of specific installation space specifications. They are particularly suitable for the early development process, where structural potential is to be systematically tapped.

FEM crash analysis is a computer-aided method for simulating structural behavior in accidents, in which the vehicle or aircraft is digitally loaded under defined crash conditions (e.g. impact speeds, angles). Using the finite element method (FEM), the behavior of individual components and materials - such as deformation, energy absorption or failure - is calculated in detail. The aim is to meet the safety requirements for occupants, structure and system integrity as well as to demonstrate compliance with legal standards and consumer protection criteria (e.g. NCAP, EASA, FAA). Optimization is carried out through variant studies on geometries, materials and load paths, whereby topology or parameter optimization is used to specifically reduce weight and improve crash performance. Especially in lightweight construction, FEM crash analysis is essential to demonstrate safety despite lower mass and to maximize weight efficiency.

The FEM-based analysis, design and optimization of sandwich systems is carried out for various materials for cover layers and cores - such as honeycomb structures or foams. FEM analyses (finite element methods) enable the realistic evaluation of the mechanical load-bearing capacity of sandwich structures with lightweight cores (e.g. aluminum honeycombs or polymer foams) and rigid cover layers (e.g. CFRP, GFRP or metals), including hybrid composites. Material modeling is used to map different behaviors such as plasticity, buckling, damage, fatigue strength behavior or viscoelastic effects of the core materials in order to accurately predict performance under bending, shear and compression loads. Optimization strategies include topology and layer structure variations to save weight under given load cases, specifically considering the interaction of cover layer and core, where fatigue strength concepts and buckling can be considered as design criteria.

The FEM-based analysis, design and optimization of fibre composite systems - especially CFRP structures - is a key tool in lightweight structural engineering. Anisotropic material properties such as the directional dependence of stiffness and strength are precisely integrated into the finite element models using special material models. The FEM simulation enables critical load paths, stress curves and potential failure areas to be identified at an early stage in order to design structures that are appropriate for their function and load. Optimization is carried out specifically via layer structure, fibre orientation and geometry - for example by adjusting topology and layer thickness - with the aim of achieving maximum weight savings while simultaneously meeting all safety and stiffness requirements. - Such methods enable mass-efficient designs that make full use of the advantages of CFRP - such as high specific stiffness - and at the same time ensure the service life of the structure through realistic fatigue strength analyses.

In the FEM-based analysis, design and optimization for impact - i.e. impact-like or crash-like loads - scenarios such as collisions or impact events are specifically mapped using special dynamic FEM simulations. The aim is to identify structural weaknesses as early as the development phase and to optimize the design in terms of inertia-critical energy absorption, deformation behaviour and safety. Optimization is achieved through targeted modification of the geometry, material selection or topology so that maximum protection and functionality is achieved with the lowest possible weight.

FEM-based analysis, design and optimization for fatigue strength is used to ensure the fatigue safety of components under cyclic loading. Numerical methods are used to determine the stress distribution under realistic load cases. The design for fatigue strength is based on the Wöhler line method, ε-N concept / strain-life method, fracture mechanics concepts, energy and damage parameters (e.g. Smith-Watson-Topper, Morrow, Brown-Miller), linear damage accumulation (Miner rule) or other methods. Safety factors and local stresses are taken into account, taking into account the influence of medium voltage, notches, joints and material properties. The aim is to ensure that a component shows no cracks or damage after a defined number of load cycles. Optimization is carried out iteratively, e.g. through shape adaptation, material selection, topology and shape changes or bionic processes, so that the component is designed to be as light as possible but at the same time fatigue-resistant.

FEM material modeling describes the mathematical representation of the mechanical behaviour of materials such as metals, plastics, fiber composites and special materials under realistic loads. Material laws are integrated into finite element models in order to simulate anisotropic, plastic, near-failure or other material behavior that has not yet been fully researched. The aim is to predict material use and structural behavior as precisely as possible. Optimization is achieved through targeted variation of geometries, wall thicknesses or fibre orientations to reduce weight while maintaining strength and rigidity. This makes it possible to develop components that only use material where it is absolutely necessary from a structural point of view or to use the material properties specifically for structural functions - a central principle of lightweight structural engineering.